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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="metric_1.html#V6" title="METRIC_1:attr.6">Reflexive</a> <a href="metric_1.html#V8" title="METRIC_1:attr.8">symmetric</a> <a href="metric_1.html#V9" title="METRIC_1:attr.9">triangle</a>  <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green" title="E37">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green" title="E38">A2</font></i>: 
not <font color="Maroon" title="c1">M</font> is <a href="tbsp_1.html#V5" title="TBSP_1:attr.5">bounded</a>
 ;<br/>

<a NAME="E3:72"/><i><font color="Green" title="E39">A3</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="txt" href="topreal6.html#E1:72"><i><font color="Green" title="E37">A1</font></i></a></i>;<br/>
<b>assume </b><a NAME="E4:72"/>
( <font color="Maroon" title="c2">X</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> &amp; <font color="Maroon" title="c3">Y</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> )
 ;<br/>

<a NAME="E5:72"/><b>then </b>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">M</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>
 
<b>by </b><i><a class="txt" href="topreal6.html#E3:72"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="tbsp_1.html#T20" title="TBSP_1:th.20">TBSP_1:20</a></i>;<br/>
<b>hence </b><a NAME="E6:72"/>
contradiction
 <b>by </b><i><a class="txt" href="topreal6.html#E2:72"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="tbsp_1.html#T25" title="TBSP_1:th.25">TBSP_1:25</a></i>;<br/>


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